It all depends on how long your child wants to spend at Platform 9 3/4 :-)
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vegemite4meJun 25 '14 at 9:44

Will you already have the tickets? Or be collecting them at the station? Or buying them? If you already have the tickets then you can arrive 15 mins before. If you're collecting them from a machine then actually you can easily get them any time after booking them. If you're buying them just before travel then you're doing it wrong ...
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TheMathemagicianJul 10 '14 at 14:40

Your train to Leeds will almost certainly leave from platforms 0-8, which are the right hand set on the map above. They're the main, long platforms used for almost all the long distance trains, and a a few of the shorter distance ones.

When you arrive at Kings Cross, you'll want to head to the main waiting area, which is the long grey area on the map that goes past the ticket office. Here you'll see some very large departure boards. Your train will typically show on here 2 hours before departure, but without a platform. Around 15 minutes before departure, depending somewhat on when the inbound train has arrived and been cleaned, the platform number will go up on the board, and they'll announce the platform. Assuming it's a 0-8 platform, you then either walk south to by the main entrance, and through the gate line there, or take the escalators by the Cafe Nero by 9-11 up, and the overbridge to drop you down onto your platforms. Even with kids and a few bags either route should be fine.

Long distance trains typically close their doors 1-2 minutes before departure, and they stop announcing the platform 2-3 minutes before departure. Without kids, don't cut it finer than about 5 minutes before departure. With kids, minimum 10 minutes.

As for how early to arrive, it depends somewhat on how you're getting there, and if your ticket can be used on other trains. If it's an Advanced Purchase ticket only valid on that train, allow extra time on your journey so you're sure you're there. 30 mins, maybe longer if it's a long way. If not, the Leeds trains are pretty frequent.

Once you're at the station, the issue you may face is that there aren't that many places to sit, and the area in front of the departure boards can be quite crowded at busy times. There's half a dozen cafes and eateries with seating, so you could head to one of those. The pub by platform 9 3/4 is busy in the evening, but in the day you should be able to get a table. On a nice day, head out the exit by platforms 9-11, and you can sit outside there, or take a short walk to the canal if you need to kill a bit more time!

The other thing to know is that St Pancras station is literally just across the road, and has slightly more in the way of shops and restaurants. It may make sense to sit down over there and have a bite to eat, then return across the road / along the underpass. Head back to KX around 15 mins before and pretty much go straight onto the train.

I would factor in about 30 minutes before departure time if you have luggage and children. In the UK it is usual for the Platform number to not be displayed until the train is ready to depart, so make sure you know where all the platforms are.